{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zPjMocS6JIUz"
   },
   "source": [
    "# Physics-Informed Neural Networks (PINNs) in Neuromancer\n",
    "\n",
    "This tutorial demonstrates the use of [PINNs](https://en.wikipedia.org/wiki/Physics-informed_neural_networks) for solving partial differential equations (PDEs) in the Neuromancer library.\n",
    "\n",
    "<img src=\"../figs/PINNs.png\" width=\"600\">  \n",
    "\n",
    "### References\n",
    "\n",
    "[1] [Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2017). Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations.](https://www.sciencedirect.com/science/article/abs/pii/S0021999118307125)\n",
    "\n",
    "[2] https://github.com/jdtoscano94/Learning-Python-Physics-Informed-Machine-Learning-PINNs-DeepONets/tree/main\n",
    "\n",
    "[3] https://github.com/omniscientoctopus/Physics-Informed-Neural-Networks/tree/main"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Y61YA90-WIZ1"
   },
   "source": [
    "## Install (Colab only)\n",
    "Skip this step when running locally."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "WZrPCr9GWEAJ",
    "outputId": "d0ff6dfe-de2a-4675-a36c-e2a7fce486d9"
   },
   "outputs": [],
   "source": [
    "# !pip install \"neuromancer[examples] @ git+https://github.com/pnnl/neuromancer.git@master\"\n",
    "# !pip install pyDOE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6k0-63d0JIU1"
   },
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "OdYMzuSDi7Js"
   },
   "outputs": [],
   "source": [
    "# import torch\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "\n",
    "# data imports\n",
    "from scipy.io import loadmat\n",
    "\n",
    "# plotting imports\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# filter some user warnings from torch broadcast\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "# neuromancer\n",
    "from neuromancer.constraint import variable\n",
    "from neuromancer.dataset import DictDataset\n",
    "from neuromancer.modules import blocks\n",
    "from neuromancer.system import Node\n",
    "from neuromancer.loss import PenaltyLoss\n",
    "from neuromancer.problem import Problem\n",
    "from neuromancer.trainer import Trainer\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "4-D966haJIU1"
   },
   "outputs": [],
   "source": [
    "#Set default dtype to float32\n",
    "torch.set_default_dtype(torch.float)\n",
    "\n",
    "#PyTorch random number generator\n",
    "torch.manual_seed(1234)\n",
    "\n",
    "# Random number generators in other libraries\n",
    "np.random.seed(1234)\n",
    "\n",
    "# Device configuration\n",
    "if torch.backends.mps.is_available():\n",
    "    device = torch.device('mps')\n",
    "elif torch.cuda.is_available():\n",
    "    device = torch.device('cuda')\n",
    "else:\n",
    "    device = torch.device('cpu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2jIhmFNMJIU1"
   },
   "source": [
    "## Problem Setup\n",
    "\n",
    "**The 2D steady-state, isotropic diffusion problem** is a classic benchmark problem in heat and mass transfer, where the Laplace equation is solved in a squared domain, under Dirichlet boundary conditions. The problem is given by  \n",
    "\n",
    "$$ \\nabla^2 \\boldsymbol{T} = 0. $$\n",
    "\n",
    "Assuming a two-dimensional space $\\Omega = [0,1] \\times [0,1]$, the temperature of the plate $T$ varies depending on the spatial position $\\boldsymbol{x}$, where $\\boldsymbol{x} = [x, y]^T$.\n",
    "\n",
    "**Boundary Conditions:**\n",
    "\n",
    "$$T(x, y=1) = T_o,$$\n",
    "$$T(x=0, y) = T(x=1, y) = T(x, y=0) = 0.$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pOe9yRvxjakj"
   },
   "source": [
    "### Sample collocation points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([200, 200])\n",
      "torch.Size([200, 200])\n"
     ]
    }
   ],
   "source": [
    "# Define number of collocation points in x and y\n",
    "Nx = 200\n",
    "Ny = 200\n",
    "\n",
    "# Define temperature at upper boundary\n",
    "To = 1.\n",
    "\n",
    "# Create collocation points\n",
    "x = torch.linspace(0, 1, Nx)\n",
    "y = torch.linspace(0, 1, Ny)\n",
    "X, Y = torch.meshgrid(x,y, indexing=\"ij\")\n",
    "print(X.shape)\n",
    "print(Y.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Qcyu8OrKJIU2"
   },
   "source": [
    "### Test data: PDE solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "WsG043OGJIU2"
   },
   "outputs": [],
   "source": [
    "X_test = X.reshape(-1,1)\n",
    "Y_test = Y.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Construct training datasets\n",
    "\n",
    "We construct training and development datasets containing [collocation points (CP)](https://en.wikipedia.org/wiki/Collocation_method) of the spatial domain (x,y), and samples of the [boundary conditions (BC)](https://en.wikipedia.org/wiki/Boundary_value_problem).\n",
    "\n",
    "The dataset is given as:\n",
    "$\\Xi_{\\text{train/dev}} = [\\texttt{CP}^i, \\texttt{BC}^j]$, $i = 1,...,N_{cp}$, $j = 1,...,N_{bp}$  \n",
    "Where $N_{cp}$ defines number of collocation points, and $N_{bc}$ number of boundary condition samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nJ_gO3xAJIU2"
   },
   "source": [
    "### Samples of boundary conditions (BC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "j2oRU6cHJIU2",
    "outputId": "bf643e73-c86a-498a-9604-33f3a8bf78e4"
   },
   "outputs": [],
   "source": [
    "# Initializing the fields\n",
    "ic_X = X[:, :]\n",
    "ic_Y = Y[:, :]\n",
    "ic_T = X[:, :] * 0.\n",
    "ic_T[:, -1] = 1.\n",
    "\n",
    "# Left boundary conditions\n",
    "left_bc_X = X[[0], :]\n",
    "left_bc_Y = Y[[0], :]\n",
    "left_bc_T = ic_T[[0], :]\n",
    "\n",
    "# Right boundary conditions\n",
    "right_bc_X = X[[-1], :]\n",
    "right_bc_Y = Y[[-1], :]\n",
    "right_bc_T = ic_T[[-1], :]\n",
    "\n",
    "# Top boundary conditions\n",
    "top_bc_X = X[:, [-1]]\n",
    "top_bc_Y = Y[:, [-1]]\n",
    "top_bc_T = ic_T[:, [-1]]\n",
    "\n",
    "# Bottom boundary conditions\n",
    "bottom_bc_X = X[:, [0]]\n",
    "bottom_bc_Y = Y[:, [0]]\n",
    "bottom_bc_T = ic_T[:, [0]]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1k6qP9nwJIU2"
   },
   "source": [
    "### Number of training samples for BC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "NO3W46OFJIU3",
    "outputId": "68cf31a7-7325-4488-e6a5-93f64fd995ab"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([800, 1]) torch.Size([800, 1]) torch.Size([800, 1])\n"
     ]
    }
   ],
   "source": [
    "X_train_bc = torch.concat([left_bc_X.flatten(), right_bc_X.flatten(), top_bc_X.flatten(), bottom_bc_X.flatten()]).view((-1,1))\n",
    "Y_train_bc = torch.concat([left_bc_Y.flatten(), right_bc_Y.flatten(), top_bc_Y.flatten(), bottom_bc_Y.flatten()]).view((-1,1))\n",
    "T_train_bc = torch.concat([left_bc_T.flatten(), right_bc_T.flatten(), top_bc_T.flatten(), bottom_bc_T.flatten()]).view((-1,1))\n",
    "print(X_train_bc.shape, Y_train_bc.shape, T_train_bc.shape)\n",
    "\n",
    "N_bc = X_train_bc.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TxOrMblXJIU3"
   },
   "source": [
    "### Samples of collocation points (CP) in the interior of the domain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "AuPDj84kJIU3",
    "outputId": "d7909693-d35c-4fc1-e0ae-7197d9027dbd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_lb = tensor([0.]), x_ub = tensor([1.])\n",
      "y_lb = tensor([0.]), y_ub = tensor([1.])\n",
      "Number of collocation points for training: 500\n",
      "Shape of X_train_cp = torch.Size([500, 1])\n",
      "Shape of Y_train_cp = torch.Size([500, 1])\n",
      "Shape of X_train = torch.Size([1300, 1])\n",
      "Shape of Y_train = torch.Size([1300, 1])\n"
     ]
    }
   ],
   "source": [
    "# Domain bounds\n",
    "x_lb = X_test[0]\n",
    "x_ub = X_test[-1]\n",
    "y_lb = Y_test[0]\n",
    "y_ub = Y_test[-1]\n",
    "print(f'x_lb = {x_lb}, x_ub = {x_ub}')\n",
    "print(f'y_lb = {y_lb}, y_ub = {y_ub}')\n",
    "\n",
    "# Choose (N_collocation) collocation Points to Evaluate the PDE\n",
    "N_cp = 500\n",
    "print(f'Number of collocation points for training: {N_cp}')\n",
    "\n",
    "# Generate collocation points (CP)\n",
    "X_train_cp = torch.FloatTensor(N_cp, 1).uniform_(float(x_lb), float(x_ub))\n",
    "Y_train_cp = torch.FloatTensor(N_cp, 1).uniform_(float(y_lb), float(y_ub))\n",
    "print(f'Shape of X_train_cp = {X_train_cp.shape}')\n",
    "print(f'Shape of Y_train_cp = {Y_train_cp.shape}')\n",
    "\n",
    "# Append collocation points and boundary points for training\n",
    "X_train = torch.vstack((X_train_cp, X_train_bc)).float()\n",
    "Y_train = torch.vstack((Y_train_cp, Y_train_bc)).float()\n",
    "print(f'Shape of X_train = {X_train.shape}')\n",
    "print(f'Shape of Y_train = {Y_train.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OwO9_mmLJIU3"
   },
   "source": [
    "### Plot CP and BC points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "kt_ItQdWJIU3",
    "outputId": "8ea18a9c-49ff-4c0b-9972-1b1c02061b96"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1400x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize collocation points for 2D input space (x, y)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(14, 6))\n",
    "ax.scatter(X_train_cp.detach().cpu().numpy(), Y_train_cp.detach().cpu().numpy(),\n",
    "            s=4., c='blue', marker='o', label='CP')\n",
    "ax.scatter(X_train_bc.detach().cpu().numpy(), Y_train_bc.detach().cpu().numpy(),\n",
    "            s=4., c='red', marker='o', label='BC')\n",
    "ax.set_title('Sampled BC and CP for training', fontsize=16)\n",
    "ax.set_xlim(x_lb.detach().cpu(), x_ub.detach().cpu())\n",
    "ax.set_ylim(y_lb.detach().cpu(), y_ub.detach().cpu())\n",
    "ax.grid(True)\n",
    "ax.set_xlabel('$x$', fontsize=16)\n",
    "ax.set_ylabel('$y$', fontsize=16)\n",
    "ax.legend(loc='upper right')\n",
    "ax.set_aspect('equal', 'box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "z6PGai8BJIU3"
   },
   "source": [
    "### Create Neuromancer datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "gUAiehD1JIU3"
   },
   "outputs": [],
   "source": [
    "# turn on gradients for PINN\n",
    "X_train.requires_grad=True\n",
    "Y_train.requires_grad=True\n",
    "\n",
    "# Training dataset\n",
    "train_data = DictDataset({'x': X_train, 'y':Y_train}, name='train')\n",
    "# test dataset\n",
    "test_data = DictDataset({'x': X_test, 'y':Y_test}, name='test')\n",
    "\n",
    "# torch dataloaders\n",
    "batch_size = X_train.shape[0]  # full batch training\n",
    "train_loader = torch.utils.data.DataLoader(train_data, batch_size=batch_size,\n",
    "                                           collate_fn=train_data.collate_fn,\n",
    "                                           shuffle=False)\n",
    "test_loader = torch.utils.data.DataLoader(test_data, batch_size=batch_size,\n",
    "                                         collate_fn=test_data.collate_fn,\n",
    "                                         shuffle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YlpywCRzJIU3"
   },
   "source": [
    "## Network architecture\n",
    "\n",
    "In this part, we use an MLP to construct a PINN that will approximate the solution of the PDE, $\\hat{T}$:\n",
    "\n",
    "$$\\hat{T} = NN_{\\theta}(x,y)$$  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "PkgSInhRJIU3"
   },
   "outputs": [],
   "source": [
    "# Neural net to solve the PDE problem bounded in the PDE domain\n",
    "# Variables in: x, y; variables out: T\n",
    "net = blocks.MLP(\n",
    "                 insize=2,                         # x and y (2 dimensions)\n",
    "                 outsize=1,                        # T(x,y) (1 dimension)\n",
    "                 hsizes=[30,30],                   # width of hidden layers\n",
    "                 nonlin=nn.SiLU                    # activation function\n",
    "                ).to(device)\n",
    "\n",
    "# symbolic wrapper of the neural net\n",
    "# Inputs: x and y\n",
    "# outputs: T\n",
    "pde_net = Node(net, ['x', 'y'], ['T'], name='net')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "symbolic inputs  of the pde_net: ['x', 'y']\n",
      "symbolic outputs of the pde_net: ['T']\n"
     ]
    }
   ],
   "source": [
    "print(\"symbolic inputs  of the pde_net:\", pde_net.input_keys)\n",
    "print(\"symbolic outputs of the pde_net:\", pde_net.output_keys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Total number of parameters = 1051\n",
      "MLP(\n",
      "  (nonlin): ModuleList(\n",
      "    (0-1): 2 x SiLU()\n",
      "    (2): Identity()\n",
      "  )\n",
      "  (linear): ModuleList(\n",
      "    (0): Linear(\n",
      "      (linear): Linear(in_features=2, out_features=30, bias=True)\n",
      "    )\n",
      "    (1): Linear(\n",
      "      (linear): Linear(in_features=30, out_features=30, bias=True)\n",
      "    )\n",
      "    (2): Linear(\n",
      "      (linear): Linear(in_features=30, out_features=1, bias=True)\n",
      "    )\n",
      "  )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "# Parameter count and structure of the network\n",
    "print(f\" Total number of parameters = {sum(p.numel() for p in net.parameters())}\")\n",
    "print(net)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sk7MKm67JIU3"
   },
   "source": [
    "###  Define physics-informed terms\n",
    "\n",
    "The neural network approximation must satisfy the PDE equation $NN_{\\theta}(x,y) \\approx T(x,y)$.\n",
    "Thus we define the residual $f$:\n",
    "\n",
    "$$f(x,y)=\n",
    " \\frac{\\partial^2 NN_{\\theta}(x,y)}{\\partial x^2} + \\frac{\\partial^2 NN_{\\theta}(x,y)}{\\partial y^2}\n",
    " $$\n",
    "\n",
    "We can obtain the derivatives of the neural net $\\frac{\\partial^2 NN_{\\theta}}{\\partial x^2},\\frac{\\partial^2 NN_{\\theta}}{\\partial y^2}$ using [automatic diferentiation](https://en.wikipedia.org/wiki/Automatic_differentiation).\n",
    "\n",
    "To simplify the implementation of $f$ we exploit the symbolic variable of the Neuromancer library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "jl65G-UwJIU3"
   },
   "outputs": [],
   "source": [
    "# symbolic Neuromancer variables\n",
    "T = variable('T')  # PDE solution generated as the output of a neural net\n",
    "x = variable('x')  # spatial coordinate 1\n",
    "y = variable('y')  # spatial coordinate 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "MvIt0hUSJIU3"
   },
   "outputs": [],
   "source": [
    "# get the symbolic derivatives\n",
    "dT_dx = T.grad(x)\n",
    "dT_dy = T.grad(y)\n",
    "d2T_dx2 = dT_dx.grad(x)\n",
    "d2T_dy2 = dT_dy.grad(y)\n",
    "\n",
    "# get the PINN form\n",
    "f = d2T_dx2 + d2T_dy2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "OqGJaQsfJIU3",
    "outputId": "468b4a57-6b02-4511-b909-e8aa3076965d"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# computational graph of f\n",
    "f.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LA4N8FukJIU6"
   },
   "source": [
    "### Loss function terms\n",
    "\n",
    "**PDE collocation points Loss:**  \n",
    "We evaluate the residual $f$ over given number ($N_{cp}$) of collocation points (CP) and minimize the PDE residuals in the following loss function:\n",
    "\n",
    "$$\\ell_{cp}=\\frac{1}{N_{cp}}\\sum^{N_{cp}}_{i=1}|f(x_c^i,y_c^i)|^2$$\n",
    "\n",
    "If $f\\rightarrow 0$ then our PINN converges to the solution of the PDE.\n",
    "\n",
    "**PDE boundary conditions Loss:**\n",
    "\n",
    "We select $N_{bc}$ points from our BC and used them in the following supervised learning loss function:\n",
    "\n",
    "$$\\ell_{bc}=\\frac{1}{N_{bc}}\\sum^{N_{bc}}_{i=1}|T(x_{b}^i,y_b^i)-NN_{\\theta}(t_{b}^i,x_b^i)|^2$$\n",
    "\n",
    "#### Total loss:\n",
    "The total loss is just a sum of PDE residuals over CP and supervised learning residuals over BC.\n",
    "\n",
    "$$\\ell_{\\text{total}}=\\ell_{cp}+\\ell_{bc}$$\n",
    "<!-- $$\\ell_{\\text{PINN}}=\\ell_{f}+\\ell_{u} +\\ell_{y}$$ -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "40DJEEfRJIU6"
   },
   "outputs": [],
   "source": [
    "# scaling factor for better convergence\n",
    "scaling_cp = 1.\n",
    "scaling_bc = 1.\n",
    "\n",
    "# PDE CP loss (MSE)\n",
    "l_cp = scaling_cp*( f == 0. )^2\n",
    "\n",
    "# PDE BC loss (MSE)\n",
    "l_bc = scaling_bc*( T[-N_bc:] == T_train_bc )^2 # remember that we concatenated CP and BC\n",
    "\n",
    "# output constraints to bound the PINN solution\n",
    "con_1 = (T >= 0) #Passive scalar T is always positive; note: this is optional"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "T1_vmWTsJIU6"
   },
   "source": [
    "##  Train the network to solve the PDE\n",
    "\n",
    "We use Adam to optimize the parameters $\\theta$ of the neural networks $NN_{\\theta}(x,y)$ approximating the solution to the PDE equation $T(t,x)$ using the total loss $\\ell_{\\text{total}}$ evaluated over sampled collocation points CP and boundary condition points BC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_Lby5wD5JIU6"
   },
   "source": [
    "### Define the optimization problem in Neuromancer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "id": "lk2wUUy4JIU6"
   },
   "outputs": [],
   "source": [
    "# Wrapper for losses and constraints\n",
    "loss = PenaltyLoss(objectives=[l_cp, l_bc], constraints=[con_1])\n",
    "\n",
    "# Vanilla PINN\n",
    "problem = Problem(nodes=[pde_net],       # list of nodes (neural nets) to be optimized\n",
    "                  loss=loss,             # physics-informed loss function\n",
    "                  grad_inference=True    # argument for allowing computation of gradients at the inference time\n",
    "                  )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "c_MoQwFBJIU6"
   },
   "source": [
    "### Construct trainers and solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "Tk4c90viJIU6"
   },
   "outputs": [],
   "source": [
    "optimizer = torch.optim.AdamW(problem.parameters(), lr=1e-3)\n",
    "\n",
    "epochs = 5001\n",
    "\n",
    "# Trainer for vanilla PINN\n",
    "trainer = Trainer(problem.to(device),\n",
    "                  train_data=train_loader,\n",
    "                  optimizer=optimizer,\n",
    "                  epochs=epochs,\n",
    "                  epoch_verbose=1000,\n",
    "                  train_metric='train_loss',\n",
    "                  dev_metric='train_loss',\n",
    "                  eval_metric=\"train_loss\",\n",
    "                  warmup=epochs,\n",
    "                  device=device)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "EWcwq4r9JIU6",
    "outputId": "b065d29c-2a51-4492-aa74-43c1b08cb429",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch: 0  train_loss: 0.3493269979953766\n",
      "epoch: 1000  train_loss: 0.03790576383471489\n",
      "epoch: 2000  train_loss: 0.025070052593946457\n",
      "epoch: 3000  train_loss: 0.024011658504605293\n",
      "epoch: 4000  train_loss: 0.023442327976226807\n",
      "epoch: 5000  train_loss: 0.023147309198975563\n"
     ]
    }
   ],
   "source": [
    "# Train vanilla PINN\n",
    "best_model = trainer.train()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate trained PINN on test data (all the data in the domain)\n",
    "pinn = problem.nodes[0].cpu()\n",
    "\n",
    "T_pinn = pinn(test_data.datadict)['T']\n",
    "\n",
    "# arrange data for plotting\n",
    "T_pinn = T_pinn.reshape(shape=[Nx,Ny]).detach().cpu()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kpRh89zM8Te8"
   },
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute the error and plot solutions\n",
    "We can compare the estimated result $\\hat{T}^*$ with the analytical solution $T_{exact}^*$:\n",
    "\n",
    "$$T_{exact}^{*} (x^*,y^*) = \\sum_{k=1}^{\\infty} \\frac{2 T_o [1-(-1)^k]}{k \\pi} \\frac{\\sin(k\\pi x^*) \\sinh(k \\pi y^*)} {\\sinh(k \\pi)}$$\n",
    "\n",
    "For evaluation purposes and to avoid numerical overflow, we truncate the series solution to $N = 200$ modes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "uo5f9_pUJIU7"
   },
   "outputs": [],
   "source": [
    "# Compute the analytical solution\n",
    "T_exact = np.zeros(shape=(Nx,Ny))\n",
    "N_modes = 200\n",
    "To = 1\n",
    "x_ = np.linspace(0, 1, Nx)\n",
    "y_ = np.linspace(0, 1, Ny)\n",
    "\n",
    "for k in range(1,N_modes):\n",
    "    for i in range(Nx):\n",
    "        for j in range(Ny):\n",
    "            T_exact[i,j] += 2 * To * (1-(-1)**k) * np.sin(k*np.pi*x_[i]) * np.sinh(k*np.pi*y_[j])/(k*np.pi * np.sinh(k*np.pi))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 2000x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot contour plots (T_exact vs T_pinn vs |T_exact - T_pinn|)\n",
    "plt.figure(figsize=(20, 6))\n",
    "\n",
    "# Plot for the first heatmap (Exact solution)\n",
    "ax1 = plt.subplot(1, 3, 1)\n",
    "cbarticks = np.arange(-0.1, 1.1, 0.05)\n",
    "CP1 = plt.contourf(ic_X.cpu(), ic_Y.cpu(), T_exact, cbarticks, cmap='viridis')\n",
    "plt.title('Exact solution, $T_{exact}$')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "plt.colorbar(CP1, label='$T$')\n",
    "ax1.set_aspect('equal', adjustable='box')\n",
    "\n",
    "# Plot for the second heatmap (PINN solution)\n",
    "ax2 = plt.subplot(1, 3, 2)\n",
    "CP2 = plt.contourf(ic_X.cpu(), ic_Y.cpu(), T_pinn, cbarticks, cmap='viridis')\n",
    "plt.title('PINN solution, $T_{PINN}$')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "plt.colorbar(CP2, label='$T$')\n",
    "ax2.set_aspect('equal', adjustable='box')\n",
    "\n",
    "# Plot for the third heatmap (Absolute error between PINN approximation and exact solution)\n",
    "ax3 = plt.subplot(1, 3, 3)\n",
    "CP3 = plt.contourf(ic_X.cpu(), ic_Y.cpu(), torch.abs(torch.Tensor(T_exact) - T_pinn), cbarticks, cmap='viridis')\n",
    "plt.title('Absolute error, $|T_{PINN} - T_{exact}|$')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "plt.colorbar(CP3, label='$T$')\n",
    "ax3.set_aspect('equal', adjustable='box')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the horizontal centerline (middle row) for both datasets\n",
    "horizontal_centerline_T_exact = T_exact[T_exact.shape[0] // 2, :]\n",
    "horizontal_centerline_T_pinn = T_pinn[T_pinn.shape[0] // 2, :]\n",
    "\n",
    "# Calculate the vertical centerline (middle column) for both datasets\n",
    "vertical_centerline_T_exact = T_exact[:, T_exact.shape[1] // 2]\n",
    "vertical_centerline_T_pinn = T_pinn[:, T_pinn.shape[1] // 2]\n",
    "\n",
    "# Create a figure and axis for the plots\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
    "\n",
    "# Plot 1: Temperature at the horizontal centerline vs. x values\n",
    "ax[0].plot(x_, horizontal_centerline_T_exact, color='black', label='$T_{exact}$')\n",
    "ax[0].plot(x_, horizontal_centerline_T_pinn, color='blue', label='$T_{PINN}$')\n",
    "ax[0].set_title('Temperature Profile at Horizontal Centerline')\n",
    "ax[0].set_xlabel('$x$')\n",
    "ax[0].set_ylabel('$T(x,y=0.5)$')\n",
    "ax[0].grid(True, linestyle=':', color='gray')  # Add dotted grid\n",
    "ax[0].legend()\n",
    "\n",
    "# Plot 2: Temperature at the vertical centerline vs. y values\n",
    "ax[1].plot(vertical_centerline_T_exact, y_, color='black', label='$T_{exact}$')\n",
    "ax[1].plot(vertical_centerline_T_pinn, y_, color='blue', label='$T_{PINN}$')\n",
    "ax[1].set_title('Temperature Profile at Vertical Centerline')\n",
    "ax[1].set_xlabel('$T(x=0.5, y)$')\n",
    "ax[1].set_ylabel('$y$')\n",
    "ax[1].grid(True, linestyle=':', color='gray')  # Add dotted grid\n",
    "ax[1].legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "collapsed_sections": [
    "Y61YA90-WIZ1",
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